The US presidential campaign of 2008 proved so enthralling that tomorrow, HBO will air a movie, Game Change, based on a single, small aspect of it: the travails of Sarah Palin, as recreated by Julianne Moore. The battle of 2012 could never hope to compete with the drama of four years ago, with its epic struggle of Obama v Hillary, pitting two historic firsts against each other. But the current Republican primary contest might nevertheless have movie potential – if only for Comedy Central.

The race has produced no end of laughs, most recently multimillionaire Mitt Romney's attempts to come across as a regular Joe. The latest was his admission that, while not himself a fan of Nascar racing – a sport that plays big in the white, male, lower-income demographic – "I have some friends who are Nascar team owners". Earlier he had sought to ingratiate himself with a Detroit audience by boasting that, as a good patriot, he drove American cars and that his wife even drove "a couple of Cadillacs". Short of wearing an "I am the 1%" T-shirt, it's hard to know how he could have got it more wrong.

And yet if that gag applies to Romney, it also applies to his entire party. This week's "Super" Tuesday, in which Romney squeaked ahead in yet another split decision, revealed a Republican party that is deeply, even structurally divided. The personality quirks of this second-rate field have hidden the extent to which the four remaining candidates represent distinct strands within Republicanism that are proving impossible to reconcile.

Romney is the embodiment of country club Republicanism, patrician, fiscally conservative, faithful to Wall Street, with roots in the more liberal north-eastern US. Santorum speaks for theo-conservatives, whose chief political creed is religion and who share his regret that the supreme court legalised contraception in 1965 and that so many women now work outside the home. Newt Gingrich is a skilled exploiter of the culture wars, though that sits alongside what the Washington Post's Anne Applebaum calls "techno-optimism", typified by Gingrich's fly-me-to-the-moon fantasies about colonising space. And lastly there is Ron Paul's undiluted libertarianism. If the Republican party cannot settle on one of these four candidates, it's partly because it cannot settle on any one of the four creeds they represent.

The party is divided along almost every axis, by religion, class and region – with Romney, the Mormon millionaire from Massachusetts on the wrong side of each line. In the past, Republicans have suppressed those divisions in order to rally behind a candidate who they believed could win. But in 2012, with the party selectorate now dominated by hardcore conservatives, they're unwilling to make that compromise.

The result, says Applebaum – who describes herself as a former Republican – is that the party is caught demanding "incompatible, impossible things": ever lower taxes, but higher military spending and untouched entitlements, especially for the elderly. It wants government to stay out of, say, the auto industry (Romney) but to get into the bedroom (Santorum). The tension between these positions is getting unbearable, with only a dogmatic loathing of the very idea of government to unite them.

When David Cameron travels to the US next week, doubtless removing his jacket and rolling up his sleeves to watch a game of college basketball in Dayton, Ohio with Obama, he will comfort himself that such headaches are an ocean away. And yet this week laid bare the divisions which – while lacking the lurid colours of the Republican fight – increasingly mark his own party.

A telling edition of Newsnight brought together a Conservative-only panel to debate the proposed mansion tax. In one corner, Jacob Rees-Mogg, whose very speech patterns signal a traditional Toryism that regards property as near sacred and to be left well alone. In the other, ConservativeHome editor Tim Montgomerie, who wants wealth, not income, to be taxed and who advised cash-poor old folks sitting in £2m houses to get a loan to pay the tax. Rees-Mogg accused Montgomerie of socialism; Twitter duly hailed him as more radical than Labour, clocking that he even wore a leftie beard.

In fact, this was not a left-right split but an internal battle neatly characterised by one Lib Dem source in the Times as Economist readers v the Country Life set. The former group is made up of unsentimental economic liberals, metropolitan in outlook, whose spiritual leader is George Osborne. The latter consists of shire Tories, who believe the countryside and property represent something more than a source of revenue. Some of them hope that, underneath all that Notting Hill modernising nonsense, Cameron belongs to their tribe.

There are other divides, too. Note the resignations this week of two below-radar Tories, Mark Pritchard and Roger Helmer MEP, over Europe. Recall that while John Major faced just nine Euro-rebels, Cameron saw 82 of his own MPs vote against him on the EU. Class plays a part too: witness Pritchard's past description of himself as a "little council house lad", or Nadine Dorries's complaint that "policy is being run by two public school boys who don't know what it's like to go to the supermarket and have to put things back on the shelves because they can't afford it … What's worse, they don't care either." Even US-style family values feature. Some of those Tories opposing the cut in child benefit to higher earners are appalled that the effect will be to punish those families where the woman has chosen to stay home to bring up the kids – precisely the values, they say, Tories should be encouraging.

Central to the problem is Cameron himself. Forced to run to the right to defeat David Davis in 2005, he led plenty of Conservatives to believe he would be one of them, on Europe and the rest. They are disappointed, "restless and disgruntled" and looking for a cause on which to fight, according to one coalition insider.

None of this equals the fratricidal viciousness currently on display in America, but what Cameron sees next week should serve as a warning to him: this is what happens when the right divides against itself.

Jonathan Freedland presents Government is Not the Solution on Radio 4, Saturday at 8pm. Twitter @j_freedland